A ball lies inside a rectangular parallelepiped in such a way that it touches three faces that have a common vertex.
| May 8, 2021 | education
A ball lies inside a rectangular parallelepiped in such a way that it touches three faces that have a common vertex. Find the distance from the center of the ball to this vertex if the volume of the ball is 34p / 3 cm3.
Points A, B and C are the tangency points of the circle centered at point O and the three side faces of the parallelepiped.
The segments ОА, ОВ and ОC are the radii of the inscribed sphere.
Let us define its radius through the volume of the sphere.
V = 32 * π / 3 = 4 * π * R3 / 3.
R ^ 3 = 3 * 32/12 = 8.
R = 2 cm.
OD is the diagonal of a cube with a side of 2 cm, then OD = OA * √2 = 2 * √2 cm.
Answer: From the center of the ball to the top of the parallelepiped 2 * √2 cm.
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